How to fix physics engine's clipping issues when modifying a mesh's shape
I believe there is a design fault in the Mesh Source area.

As we switch source to deform, the checkbox deforming appears.


  Deforming
  Mesh shapes can deform during simulation.


That's what we need, because right now, the simulation only utilizes the cube's shape of the starting frame. Enable the deforming checkbox.



Now your rigid body simulation will respect the change in deformation caused by the Displace Modifier and update the movement accordingly. (The cube bounces.)

Even when you switch the Source property back to Final the change in geometry is respected. I'm guessing someone forgot to display the Deforming checkbox as well when the Source is set to final. Even though it is not shown, is value is still used.

The difference with the two option can be researched in the manual:
Deform
Includes any deformations added to the mesh (shape keys, deform modifiers).


  Deform
  Includes any deformations added to the mesh (shape keys, deform modifiers).
  
  Final
  Includes all deformations and modifiers.


Since the displacement modifier is a Deform modifier, you don't have to switch the source property to Final. Leaving it on Deform makes no difference, but has the advantage of being aware of the Deforming checkbox.


Displacement is a Deform modifier.